Theory of invariants and applications

不变量理论及其应用

• 批准号: 5285-2007
• 负责人: Djokovic, DragomirZ
• 金额: $ 1.17万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=420041
• 关键词: Theory; invariants; applications

We shall analyze the structure of the algebra of polynomial invariants of a classical group G such as GL_n, SO_n, O_n and Sp_{2n} acting on pairs of matrices (X,Y) of appropriate size (n or 2n) by simultaneous conjugation. In particular our intention is to compute (for some small values of n) the Poincare series, a minimal set of homogeneous generators, a homogeneous system of parameters, the corresponding Hironaka decomposition and also to describe the Hilbert's null-cone for the action. Such explicit results are known only in a handful of cases and it is important to have these data available for various applications. For instance these results may be used in the study of algebras satisfying polynomial identities.

本文分析了经典群G（GL_n，SO_n，O_n和Sp_{2n}）的多项式不变量代数通过同时共轭作用于适当大小（n或2n）的矩阵对（X，Y）的结构。特别是我们的意图是计算（对于一些小的值n）庞加莱级数，一个最小的齐次发电机，一个齐次系统的参数，相应的Hironaka分解，并描述希尔伯特的零锥的行动。这种明确的结果只在少数情况下是已知的，重要的是要有这些数据可用于各种应用。例如，这些结果可用于研究代数满足多项式恒等式。